We targeted galaxies at \(z=2.86\) –\(4.44\)  (excluding the \(\mbox{Ly$\alpha $}\)  redshift range in the AO gap) to investigate their \(\mbox{Ly$\alpha $}\)  haloes. There are two main reasons for this redshift range choice. First, at \(z\le 4.7\)  for \(\mbox{Ly$\alpha $}\)  (4700–7000 Å), the background noise level is stable compared to those at longer wavelengths (see the black shaded area indicating \(z\ge 4.44\)  in Figure REF a). The 5\(\sigma \)  median SB noises for the typical parameters for the halo search (see Section REF ) at \(z=2.86\) –\(4.44\)  are shown in Figure REF b. Second, at \(z\le 4.44\) , the HST band ACS/WFC \(F775W\)  can capture the UV continuum of galaxies without being contaminated by \(\mbox{Ly$\alpha $}\)  emission [1]}, [2]}. In fact, [3]} reported that some local galaxies show a wide \(\mbox{Ly$\alpha $}\)  absorption feature, which could extend to \(\lambda \simeq 1260\)  Å. These features were also confirmed at high redshifts [4]}. The threshold of \(z=4.44\)  for rest-frame 1270 Å corresponds to 6900 Å, at which \(F775W\)  filter has 3% transmission [5]}. In addition, we limited the field to the very deep area with 100- to 140-hour integration (\(r<31\)  arcsec) to have a homogeneous depth.
